A compressor unit is known from DE-U-92 15 231. In this prior compressor unit, a centering rim is provided on the individual housing halves which is radially outside the housing region forming the side channel. When the individual side-channel compressors are assembled into a unit, the side-channel compressors are centered with respect to one another by the respective inner housing halves which engage in one another via their centering rims. Attachment of the housing halves belonging to each side-channel compressor occurs via attachment brackets provided on the outer periphery of these housing halves into which attachment screws are inserted. The attachment brackets adjoin the inner parting plane of the two housing halves. For attachment of the side-channel compressors themselves, there are provided, on the outer periphery of the mutually facing housing halves of these side-channel compressors, attachment brackets adjoining the outer parting plane of those housing halves, into which attachment screws are once again inserted. With this type of attachment, only compressors with identical outside dimensions can be joined together into a unit.